(3x+1)(x-1)-3(x+2)=-9

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Solution for (3x+1)(x-1)-3(x+2)=-9 equation: 


Simplifying
(3x + 1)(x + -1) + -3(x + 2) = -9

Reorder the terms:
(1 + 3x)(x + -1) + -3(x + 2) = -9

Reorder the terms:
(1 + 3x)(-1 + x) + -3(x + 2) = -9

Multiply (1 + 3x) * (-1 + x)
(1(-1 + x) + 3x * (-1 + x)) + -3(x + 2) = -9
((-1 * 1 + x * 1) + 3x * (-1 + x)) + -3(x + 2) = -9
((-1 + 1x) + 3x * (-1 + x)) + -3(x + 2) = -9
(-1 + 1x + (-1 * 3x + x * 3x)) + -3(x + 2) = -9
(-1 + 1x + (-3x + 3x2)) + -3(x + 2) = -9

Combine like terms: 1x + -3x = -2x
(-1 + -2x + 3x2) + -3(x + 2) = -9

Reorder the terms:
-1 + -2x + 3x2 + -3(2 + x) = -9
-1 + -2x + 3x2 + (2 * -3 + x * -3) = -9
-1 + -2x + 3x2 + (-6 + -3x) = -9

Reorder the terms:
-1 + -6 + -2x + -3x + 3x2 = -9

Combine like terms: -1 + -6 = -7
-7 + -2x + -3x + 3x2 = -9

Combine like terms: -2x + -3x = -5x
-7 + -5x + 3x2 = -9

Solving
-7 + -5x + 3x2 = -9

Solving for variable 'x'.

Reorder the terms:
-7 + 9 + -5x + 3x2 = -9 + 9

Combine like terms: -7 + 9 = 2
2 + -5x + 3x2 = -9 + 9

Combine like terms: -9 + 9 = 0
2 + -5x + 3x2 = 0

Factor a trinomial.
(2 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.6666666667, 1}

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